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To obtain the unknown intermediate vector function needs to solve a Fredholm integral equation of the first kind, the solution of which can only be determined with a difference of a vector proportional to the normal of the boundary and its integration on the boundary must zero.

可是要求出该积分表达式中待定的边界上的向量密度函数要导致求解第一类Fredholm 积分方程。

Methods From the fundamental equation in Laplace domain, using Multiple Reciprocity Method-Boundary Element Method, the integral equations and the boundary integral equations are derived and solved numerically.

方法由 Laplace 变换域中的基本方程出发，利用多重互换边界元方法，得到了积分方程和边界积分方程，并求得数值解。

After making the gauge transformation, the effect of long range interaction is equivalent to twisting the boundary field, and the expressions of the boundary condition are given. The induced model is similar to the one which contans Aharonov-Bohm effect potential.

通过引入与构型相关的酉变换，我们成功地将该系统转化为能够直接求解的类型，得到这种长程相互作用的效果相当于产生扭曲边界场，并给出了扭曲边界的具体形式，指出模型类似于具有Aharonov-Bohm效应势的Bariev模型。

Taking advantage of gauge transformation and dipolar approximation, we qualitatively derive rotating Bose-Hubbard model.Then finite temperature phase boundary between superfluid phase and normal state in rotating Bose-Hubbard model is analytically derived by studying the stability of normal state in rotating bosonic optical lattice.We also analytically prove that as the function of rotation angular velocity the oscillation of critical hopping matrix directly follows the upper boundary of Hofstadter butterfly.

4通过做一个规范变换和偶极近似，定性地推导了旋转Bose-Hubbard模型，并且通过研究正常态不动点的稳定性推广了旋转Bose-Hubbard模型的零温相图到有限温度的情形；另外根据系统有效的能带宽度与旋转速度的关系(Hofstadter蝴蝶)，得到了系统的临界跃迁矩阵随旋转速度的改变展示谐振行为的结论。

Differing from the general BEM that is attributed from the general boundary integral equation, The natural boundary element method attributed from the natural BIE has not only the advantage of the dimensionality, but is confirmed and gain the only NBIE from the original problem.

无网格方法仅仅需要节点信息，克服了有限元等传统数值方法对网格有较强依赖性的缺点，摆脱了网格的束缚，避免了大量的网格分划、复杂的网格生成及重新划分的工作，减少了因网格畸变而引起的困难，而且收敛快、精度高、易于实现和进行后处理工作。

According to the boundary condition of the actual rectangular plates, it is very easy to get the characteristic equation for the problem through the boundary value of the generalized solution.

根据实际矩形板的边界条件，再应用弹性矩形薄板稳定问题的广义位移解的边界值，很容易便可得到该稳定问题的特征方程。

Himalaya, which formed on the basement of the Pan-African orogenic event at about 550 Ma BP and experienced Ordovician to Devonian platform sedimentation, was transformed into to a back-arc extensional-rifted zone at the end of the Carboniferous. The Yarlung Zangbo ophiolitic mélange zone is a Mesozoic back-arc spreading basin corresponding to the Gangdise paleo-island arc zone on the south side of the Tethyan Ocean. The Gangdise zone experienced island-arc orogeny in the Late Paleozoic. The very significant differences in geology on both sides of the Bangong Co-Nujiang suture zone suggest that the suture zone is not only the northern boundary of Gondwanaland and the boundary between the Indian (Yunnan-Tibet) stratigraphic realm and the South China (Qiangtang-Sanjiang) stratigraphic realm, but also the relics of subductional collision and final extinction of the Phanerozoic Tethyan Ocean after the breakup of the Neoproterozoic supercontinent Rodinia. The basic point of study of the collisional orogenic processes of the plateau is the structure and composition of the archipelagic arc-basin tectonic realm of three different stages bounded by three rigid paleocontinental blocks (Gondwanaland, Laurasia and Pan-Cathaysian) and the mutual constraining, transformation and coupling of various material movement forms.

喜马拉雅奠基于5.5亿年左右的泛非造山事件基底上，历经奥陶纪至泥盆纪台地沉积，并于石炭纪末转化为印度板块北缘的弧后伸展裂陷带；雅鲁藏布江蛇绿混杂岩带曾是特提斯大洋南侧与冈底斯古岛弧带相对应的中生代弧后扩张盆地；冈底斯带曾经历了晚古生代岛弧造山作用；班公湖-怒江带两侧大量地质特征重大差异表明，班公湖-怒江带是冈瓦纳大陆北界，是印度地层区和华南地层区的分界，是新元古代Rodinia超大陆解体后显生宙特提斯大洋俯冲，消减，碰撞，最后消亡的遗迹。

There are various complex interactive relationships between the original system and the environment system in an expending system; therefore the band boundary becomes a gradational boundary.

在全系统中，由于本体系统与环境系统之间会产生各种各样非常复杂的相互作用关系，因而本体系统的边界就成了一个具有丰富层次的环带边界。

On one hand, the grain boundaries are the sites of microcrack nucleation, microcracks first occur at grain boundary zone, whose propagation type depends on lamellar orientation of both side of grain boundary.

一方面，微裂纹首先萌发于晶界区，其扩展方式取决于晶界两侧片层的取向。

Boundary representation, involves actually drawing the boundary of the model so that it appears on the display of a graphics terminal.

界限表示法，介入实际上得出模型的界限，以便它在图形终端的显示出现。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新